In a variety of communications systems, such as for example, wireless communications systems, a signal or signal burst is transmitted in which a portion of the signal burst transmitted is predetermined or known prior to transmission, referred to in this context as the "midamble," as illustrated in FIG. 6; however, a portion of the signal burst transmitted is also unknown. Typically, the known portion of the transmitted signal burst is received at the receiving end of the communications system, along with the unknown portion, and the known portion may then be employed to obtain an estimate of the communications channel for further signal processing of the unknown portion of the signal burst.
Such channel estimation is particularly useful in wireless communications systems employing modulation techniques in which binary digital signals or bits are encoded for transmission via a wireless medium. Examples of such modulation techniques include Minimum Phase Shift Keying (MSK) and Gaussian Minimum Phase Shift Keying (GMSK), although the invention is not limited in scope in this respect. Typically, a baseband modulated signal is applied to a carrier signal for transmission via the wireless medium. In this context, "a wireless communications system" refers to a communications system having a transmitting end and a receiving end in which signals are transmitted or communicated from the transmitting end to the receiving end via a signal path, a portion of the signal path from the transmitting end to the receiving end including signal transmission via a wireless medium.
Once a channel estimate is obtained at the receiving end of the communications system, typically an estimate of the signal transmitted is reconstructed from the dot product of the channel estimate with vectors representing the Viterbi states for the particular modulation scheme employed, where Viterbi decoding is employed at the receiving end of the communications system to perform equalization. Such an approach is computationally intensive, often resulting in more time than is desirable for signal processing. Furthermore, this processing may take place in an environment in which processing time is an important resource to be conserved. A need therefore exists for a more efficient method of performing signal reconstruction at the receiving end of a communications system.